Problem 31: The parallel circuit depicts three resistors connected to a voltage source.
The voltage source (AVtot) is a 110.-V source and the resistor values are
15.4 QR1), 21.9 D (R2) and 11.7 Q (R3).
b. Determine the current in each branch resistor.
c. Determine the total current in the circuit.

Bi. Current in 15.4 Ω (R₁) is 7.14 A.

Bii. Current in 21.9 Ω (R₂) is 5.02 A.

Biii. Current in 11.7 Ω (R₃) is 9.40 A.

C. Total current in the circuit is 21.56 A.

Explanation:

Bi. Determination of the current in 15.4 Ω (R₁)

Voltage (V) = 110 V

Resistance (R₁) = 15.4 Ω

Current (I₁) =?

V = I₁R₁

110 = I₁ × 15.4

Divide both side by 15.4

I₁ = 110 / 15.4

I₁ = 7.14 A

Therefore, the current in 15.4 Ω (R₁) is 7.14 A.

Bii. Determination of the current in 21.9 Ω (R₂)

Voltage (V) = 110 V

Resistance (R₂) = 21.9 Ω

Current (I₂) =?

V = I₂R₂

110 = I₂ × 21.9

Divide both side by 21.9

I₂ = 110 / 21.9

I₂ = 5.02 A

Therefore, the current in 21.9 Ω (R₂) is 5.02 A

Biii. Determination of the current in 11.7 Ω (R₃)

Voltage (V) = 110 V

Resistance (R₃) = 11.7 Ω

Current (I₃) =?

V = I₃R₃

110 = I₃ × 11.7

Divide both side by 11.7

I₃ = 110 / 11.7

I₃ = 9.40 A

Therefore, the current in 11.7 Ω (R₃) is 9.40 A.

C. Determination of the total current.

Current 1 (I₁) = 7.14 A

Current 2 (I₂) = 5.02 A

Current 3 (I₃) = 9.40 A

Total current (Iₜ) =?

Iₜ = I₁ + I₂ + I₃

Iₜ = 7.14 + 5.02 + 9.40

Iₜ = 21.56 A

Therefore, the total current in the circuit is 21.56 A

The bicyclist turning around a corner

Explanation:

Acceleration is caused by either change in magnitude or direction of the velocity of a body. Acceleration is given by rate of change of velocity over time. Hence, for acceleration to have a non-zero value, the velocity of the object must change.

In case 2, the car is in cruise control, which is basically a constant velocity motion and also the direction of motion is fixed i.e. south, hence no acceleration.

In case 3, the bus is travelling at a constant speed towards north i.e. fixed speed and fixed direction. Again, no acceleration.

In case 4, the helicopter is waiting to take off, i.e. it is at rest, with velocity 0. Hence, no acceleration.

However, in case 1, the bicyclist is turning around a corner which is circular motion. Although the velocity magnitude might be constant, its direction is continuously changing along the corner. Hence, the bicycle is accelerating.